Enantiotropic systems

The importance of temperature-controlled scanning calorimetry for measurements of heat capacity and of scanning transitiometry for simultaneous caloric and pVT analysis has been demonstrated for polymorphic systems [9]. This approach was used to study an enantiotropic system characterized by multiphase (and hindered) transitions, the role of heat capacity as a means to understand homogeneous nucleation, and the creation of (p, T) phase diagrams. The methodology was shown to possess distinct advantages over the more commonly used combination of characterization techniques. 

Figure 8.40 Free energy vs. temperature diagrams for two polymorphs (forms I and II) showing free energy crossing points (a) enantiotropic system (b) monotropic system.

However, diffraction methods have severe drawbacks. Disordered crystals are often difficult to tackle. If the disorder is of dynamic nature, e.g. arising from small-or large-amplitude motions in the crystal, the use of devices for variable-temperature measurements is compulsory and can also yield very useful information (see below for some examples) on the existence of enantiotropic systems related by phase transitions. In some, not frequent, cases the crystals are sufficiently robust to be used for direct phase transition measurements on the diffractometer. Figure 3 shows an example of multiple diffraction data sets collected on the same specimen... 

Order-to-Order Phase Transitions Between Enantiotropic Systems... 

Fig. 2.3 Energy vs temperature (E/T) diagram of a dimorphic system. G is the Gibbs free energy and H is the enthalpy. This diagram represents the situation for an enantiotropic system, in which Form I is the stable form below the transition point, and presumably at room temperature, consistent with the labelling scheme for polymorphs proposed by McCrone (see Chapter 1). (Adapted from Grunenberg et al. 1996, with permission.)...

Fig. 2.6 Pressure vs temperature plots. I/v. and II/v. represent sublimation curves I.v. is the boiling point curve. Broken lines represent regions which are thermodynamically unstable or inaccessible, (a) enantiotropic system (b) monotropic system. The labelling corresponds to earlier figures to indicate that Form I is stable at room temperature which is below the transition point in the enantiotropic case. (From McCrone 1965, with permission.)...

Obtaining the thermodynamically stable form in an enantiotropic system precautions must be taken to maintain the thermodynamic conditions (temperature, pressure, relative humidity, etc.) at which the G curve for the desired polymorph is below that for the undesired one. 

Obtaining the thermodynamically metastable form in an enantiotropic system the information for obtaining and maintaining this form is essentially found in the energy-temperature diagram. 

Enantiotropic systems LT = low-temperature form, HT = high-temperature fortiL Monotropic systems S = stable form, MS = metastable form. 

Figs. 6A and B illustrate the plots of the functions G and H versus temperature (energy/temperature diagrams) for each polymorph and for the liquid. The thermodynamic reversibility of the solid transition between two crystalline forms is characteristic of enantiotropic systems. Each form has its thermodynamic stability range. The lower melting form is... 

The thermodynamic activity of each crystalline form, represented by its solubility, may change quite differently as a function of temperature. Monotropic systems are dehned as systems where a single form is always more stable regardless of the temperature. Enantiotropic systems are dehned as systems where the relative stability of the two forms inverts at some transition temperature (Bym et al., 1999). 

Figure 6 Enantiotropic system as a function of temperature (x-axis).

Figure 1 Energy-temperature diagrams, (a) For a hypothetical enantiotropic system T and T, melting points of forms I and II 7, transition temperature, (b) For a hypothetical monotropic system 7 and 7n, melting points of forms I and II.

FIGURE 3.3 Schematic DSC traces showing the thermal behavior of enantiotropic systems under four sets of conditions (a) solid state transformation of 11 to 1 followed by melting of 1, (b) melting of metastable 11 followed by recrystallization to 1, (c) solid-state transformation of 1 to 11 followed by reverse transformation at T0, with melting at TM1 and (d) persistence of metastable 1 below T0 followed by melting at TM1. (Based on Giron, D., Thermochim. Acta, 248, 1, 1995.)... 

Enantiotropic systems whose transition temperatures fall within normal processing temperature ranges must be characterized in order to develop robust crystallization methods. The crystallization of a substance above its transition temperature can afford a form that is metastable under ambient conditions. Regardless of which form is desired, knowing the transition temperature is critical to planning the crystallization. 

If as shown in Fig. 10 one polymorph is stable (i.e., has the lower free energy content and solubility over a certain temperature range and pressure), while another polymorph is stable (has a lower free energy and solubility over a different temperature range and pressure), the two polymorphs are said to be enantiotropes, and the system of the two solid phases is said to be enantiotropic. For an enantiotropic system a reversible transition can be observed at a definite transition temperature, at which the free energy curves cross before the melting point is reached. Examples showing such behavior include acetazolamide, carbamazepine, metochlopramide, and tolbutamide [9,14,15]. 

Ostwald s step rule [13,16-19] is illustrated by Fig. 12. Let an enantiotropic system (Fig. 12a) be initially in a state represented by point X, corresponding to an unstable vapor or liquid or to a supersaturated solution. If this system is colled, the Gibbs free energy will de-... 

Relationship between the Gibbs free energy G and the temperature T for two polymorphs for (a) an enantiotropic system and (b) a monotropic system in which the system is cooled from point X [9]. The arrows indicate the direction of change. (Reproduced with permission of the copyright owner, Elsevier, Amsterdam,... 

The 8,-82-V triple point is one at which the reversible transformation of the crystalline polymorphs can take place. If both 8, and 82 are capable of existing in stable equilibrium with their vapor phase, then the relation is termed enantiotropy, and the two polymorphs are said to bear an enantiotropic relationship to each other. For such systems, the 8,-82-V triple point will be a stable and attainable value on the pressure-temperature phase diagram. A phase diagram of a hypothetical enantiotropic system is shown in Fig. 7. Each of the two polymorphs exhibits a 8-V sublimation curve, and they cross at the same temperature at which they meet the 8,-82 transition curve. The 82-V curve... 

It should be noted that the ordinary transition point of enantiotropic systems (which is measured at atmospheric pressure) will be less than the melting point of either solid phase. Each polymorph will therefore be characterized by a definite range of conditions under which it will be the most stable phase, and each form is capable of undergoing a reversible transformation into the other. 

The melting behavior of an enantiotropic system is often interesting to observe. If one begins with the polymorph that is less stable at room temperature and heats the solid up to its melting point, the S2-L melting phase transformation is first observed. As the temperature is raised further, the melt is observed to resolidify because the liquid is metastable with respect to the most stable polymorph, Sj. Continued heating will then result in the Sj-L phase transformation. If one allows... 

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